busted phone or fixable...?

Hello guys, I just got my UNLOCKED galaxy s4 a few days ago. Immediately after unboxing it and connecting to wifi it told me there was an update so I updated it (never again installing updates that aren't required to actually run the device). Anyways I'm having a terrible experience with the phone, and was wondering if there is any way to solve this without having to return the phone as I am going in vacation soon.
Problems:
Extremely short battery life - 3-4 charges per day
LONG time to charge - about 6 hours to fully charge
Keeps thinking phone is plugged in - if I plug out the charger the phone stays as being plugged in. Only way to fix this is to turn off phone and take out the battery and restart it, then its ok but battery life still super short.
Terrible signal - both wifi and my network (simple mobile, phone is unlocked) are extremely low. WIth my old ****ty phone I always had 5 bars in my dorm now I have like 3 max and it sometimes disconnects (in placements like basements I dont get signals at all). Wifi is also constantly disconnecting

I'm almost sure it's a flawed update. Everything else works perfectly, phone is super sweet blah blah... but at this state it's unusable in the long run. I restored the phone to factory settings and nothing... any tips?
Returning the phone is last last laaaast resort
Thanks

Hello guys, I just got my UNLOCKED galaxy s4 a few days ago. Immediately after unboxing it and connecting to wifi it told me there was an update so I updated it (never again installing updates that aren't required to actually run the device). Anyways I'm having a terrible experience with the phone, and was wondering if there is any way to solve this without having to return the phone as I am going in vacation soon.
Problems:
Extremely short battery life - 3-4 charges per day
LONG time to charge - about 6 hours to fully charge
Keeps thinking phone is plugged in - if I plug out the charger the phone stays as being plugged in. Only way to fix this is to turn off phone and take out the battery and restart it, then its ok but battery life still super short.
Terrible signal - both wifi and my network (simple mobile, phone is unlocked) are extremely low. WIth my old ****ty phone I always had 5 bars in my dorm now I have like 3 max and it sometimes disconnects (in placements like basements I dont get signals at all). Wifi is also constantly disconnecting

I'm almost sure it's a flawed update. Everything else works perfectly, phone is super sweet blah blah... but at this state it's unusable in the long run. I restored the phone to factory settings and nothing... any tips?
Returning the phone is last last laaaast resort
Thanks

Flashing official rom with odin Will not void the warranty. But do not downgrade

Press THANK YOU and LIKE button if you gets the answer

okay. Can I get some links, sorry I looked for s4 i9500 roms and I found the google version 4.2.2 and whatever, but that's what I have now what is the original official rom?.. apparently I have to root the device (no clue) also I heard this won't let me download/update apps? Can I go to the official version once they fix it?

okay. Can I get some links, sorry I looked for s4 i9500 roms and I found the google version 4.2.2 and whatever, but that's what I have now what is the original official rom?.. apparently I have to root the device (no clue) also I heard this won't let me download/update apps? Can I go to the official version once they fix it?

you will not get ota update when you root your phone . also reflashing will remove root from your phone. remember do not downgrade your phone while flashing this will damage efs folder